As an important tool for performance assessment in multi-state systems, the universal generating function approach is introduced and developed aiming at strength reliability analysis of structural systems. Static reliability models of statically determinate and statically indeterminate systems are built by constructing special generating functions, which are used to describe probability distrib...

This paper studies the behavior of a discrete queueing system which accepts synchronized arrivals and provides synchronized services. The number of arrivals occurring at an arriving point may follow any arbitrary discrete distribution possessing finite first moment and convergent probability generating function in I z [ ~< 1 + e with e > O. The system is equipped with an infinite buffer and one...

In this paper we study polynomial and geometric (exponential) ergodicity forM/G/1-type Markov chains and Markov processes. First, practical criteria for M/G/1-type Markov chains are obtained by analyzing the generating function of the first return probability to level 0. Then the corresponding criteria for M/G/1-type Markov processes are given, using their h-approximation chains. Our method yie...

This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit of the cumulant generating function of codeword lengths allowing positive excess distortion probability. It is shown that the achievability and converse bound...

Consider a nite alphabet with a probability distribution p. We study the probability (p) of obtaining a palindrome in a nite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed form expression for (p). Moreover we describe completely the cases where (p) has value less than 1, in connection with the singularities of the generating function. ...

This paper investigates the problem of variable-length source coding with criteria normalized cumulant generating function codeword lengths and excess distortion probability. We analyze non-asymptotic fundamental limit under constraint that probability is allowed up to ϵ ∈ [0, 1). Our achievability converse bounds are characterized by quantity related Rényi entropy.